An inductance of 0.5 H, a capacitance of `1muF` and a resistance of 100 `Omega` are connected in series and a source of A.C. emf of r.m.s. value 20 V and frequency 50 Hz is connected across the combination. The average power consumed over one cycle is

Options

A. 0.0044 W
B. 0.255W
C. 2.55 W
D. 5.25 W

Answer

A

Explanation

`X_(L)=2pifL`
`=2xx3.14xx50xx0.5`
`=157Omega`
`X_(C)=(1)/(2pifC)`
`=(1)/(2xx3.14xx50xx1xx10^(-6))=3184Omega`
`Z=sqrt(R^(2)+(X_(L)-X_(C))^(2))`
`=sqrt(100^(2)+(157-3184)^(2))=3028.6Omega`
`I_(rms)=(e_(rms))/(Z)=(20)/(3028.6)=0.006603A`
`cosphi=(R)/(Z)=(100)/(3028.6)=0.03301`
Thus, power consumed in one cycle is,
`overline(P)=e_(rms)I_(rms)cosphi`
`=20xx0.006603xx0.03301`
`~~0.0044W`